Verifying Inverse Functions | Precalculus

This precalculus video tutorial explains how to verify inverse functions. It discusses how to determine if two functions are inverses of each other by checking the composite functions of f(x) and g(x) to see whether or not it's equal to x. This video contains plenty of examples and practice problems.
Introduction to Functions:
• Functions - Vertical L...
Evaluating Functions:
• Evaluating Functions -...
Function Operations:
• Function Operations
Increasing and Decreasing Functions:
• Increasing and Decreas...
Relative Maximum & Minimum Values:
• Identifying The Relati...
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Relations and Functions:
• Relations and Function...
Domain and Range From a Graph:
• Domain and Range of a ...
How To Find The Domain of a Function:
• How To Find The Domain...
Average Rate of Change of a Function:
• Average Rate of Change...
The Difference Quotient of a Function:
• Difference Quotient
_____________________________________
Evaluating Piecewise Functions:
• Evaluating Piecewise F...
Graphing Piecewise Functions:
• Graphing Piecewise Fun...
Composite Functions:
• Composite Functions
How To Evaluate Composite Functions:
• How To Evaluate Compos...
Composite Functions - Data Table:
• How To Evaluate Compos...
Comp. of 3 Functions - Data Table:
• Composition of Three F...
Decomposing Functions:
• Decomposing Functions ...
_________________________________
Introduction to Inverse Functions:
• Introduction to Invers...
How To Find The Inverse of a Function:
• How To Find The Invers...
Verifying Inverse Functions:
• Verifying Inverse Func...
Horizontal Line Test - 1 to 1 Functions:
• Horizontal Line Test a...
Vertical Line Test:
• Vertical Line Test
Graphing Inverse Functions:
• Graphing Inverse Funct...
Composite and Inverse Functions:
• Composite Functions an...
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Even and Odd Functions:
• Even, Odd, or Neither ...
Transformations of Functions:
• Transformations of Fun...
Linear Functions:
• Linear Functions
Functions and Graphs - Problems:
• Functions and Graphs |...
Functions - Test Review:
• Functions
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Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

Next Video: kzbin.info/www/bejne/bKacgptni86Sh9k Final Exams and Video Playlists: www.video-tutor.net/ Functions and Graphs: kzbin.info/www/bejne/kIWop2uFo6yUrtE Transformations of Functions: kzbin.info/www/bejne/qqq0faNsrZJ6pbc Graphing Polynomial Functions: kzbin.info/www/bejne/qICylpmaprKpqqM

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[@NumberNinjaDave]

So easy to understand. We do need to point out that the assumption here is that we've restricted the domain, since taking the square root of a function normally yields +/- square root. These functions usually also fail the horizontal line test and by default, don't have an inverse function but a relation.

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[@oleksandrmarkovichenko5774]

Wow, that's the reason why people struggle with math so much - instructors just don't know/understand what they trying to teach. 2:12 sqrt(x^2) is not equal to x. It is |x| and that's why these two functions are actually NOT inverse. To make them inverse, you need to change the domain of f(x) to x>0, and in this case, sqrt(x^2) is equal to x

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[@maxkennedy7525]

The two functions in your first example are, sadly, NOT inverses unless you restrict the domain of f(x). For example, if x = -2, then g(f(x)) = 2, not -2, so it is not always the case that g(f(x)) = x. Please update the video to either mention the domain restriction that x >= 0, or scrap the first example, so I can share an otherwise good instructional video with my students! :)

[@cormacapostolides4260]

what does this mean

[@creed8047]

@@cormacapostolides4260 square root of x can't be x itself,it is the absolute value of x. For square root of x to ve x itself,x should be greater than or equal to 0. Take square root of -2² as example. It cam't be -2,right?

[@nerdreturn9528]

Don’t you just automatically use the positive root as it’s the principal root? So in his first example it’s +/- x but you just use x not -x?

[@ajmal_pro07]

I think...when working with composite functions...the range of g(x) would be domain of f(x)...and here...g(x) would always be positive and x always greater or equal to 5... So the input of f(x) would always be positive and the graph always on the Right...

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[@alvinshen9501]

I have a question, what if one of the functions have a restriction. For example , ( if X is greater than or equal to zero)

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That is how the first question should've been

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[@dunnomuch-7875]

Can they be inversed with eachother if both answer equals to negative x?

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[@Info_rare]

2:25 square root of x^2 is absolute x which is + or - x

[@jesiryt8583]

So you have to test both composite functions??

[@seriousnesstv7902]

No if one gets you x then you know they are both inverse

[@user-in6qc4gx8g]

8:38 / 12:05

[@devonc2867]

3:43

[@katelynns4887]

Is there a reason why it has to equal to x?

[@EmpyreanLightASMR]

8:54 Just be careful you don't let the parentheses confuse you. He's using the parentheses as a placeholder here, because otherwise it looks like (5/x + 3) times -3, which isn't the case. The line is simply 5/x + 3 - 3. Maybe it would make more sense to use a large underline or something, since parentheses usually denote multiplying. Edit: Like others have said, this video is not entirely accurate. First and last examples (anything with roots: square root, cube root, etc) you're beginning to deal with limitations. x can represent anything, but if it represents a negative number, then you're running into problems. He has better videos explaining this elsewhere, probably earlier in this pre-calc playlist.

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[@A_Dilophosaurus]

Pray for me I got a quiz on this tomorrow

[@sujashnayak1773]

Is there any proof for this?

[@jsr79080]

Hey all, this is not accurate. A quadratic function is not one to one and therefore does not have an inverse. Hope he can take this down and put up a better problem

[@KimChaewon-on2ig]

what if it is -x? is it inverses?

[@Joe-qt3hw]

The second method didnt rhyme with the first method in the last two examples

[@danielmartin7210]

A funtion that is not a BIJECTION doesnt have an inverse! Please... Is f(x)=x^2+5 one-to-one???

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